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A248906 Binary representation of prime power divisors of n: sum(p^k | n, 2^(A065515(p^k)-1)). 2

%I #12 Mar 07 2015 15:01:33

%S 0,1,2,5,8,3,16,37,66,9,128,7,256,17,10,549,1024,67,2048,13,18,129,

%T 4096,39,8200,257,16450,21,32768,11,65536,131621,130,1025,24,71,

%U 262144,2049,258,45,524288,19,1048576,133,74,4097,2097152,551,4194320,8201

%N Binary representation of prime power divisors of n: sum(p^k | n, 2^(A065515(p^k)-1)).

%H Reinhard Zumkeller, <a href="/A248906/b248906.txt">Table of n, a(n) for n = 1..10000</a>

%F Additive with a(p^k) = sum(j=1,k,2^(A065515(p^j)-1).

%F a(A051451(k)) = 2^k - 1.

%F a(n) = sum(2^(A095874(A210208(n,k))-2): k = 1..A073093(n)). - _Reinhard Zumkeller_, Mar 07 2015

%e The prime power divisors of 12 are 2, 3, and 4. These are indices 1, 2, and 3 in the list of prime powers, so a(12) = 2^(1-1) + 2^(2-1) + 2^(3-1) = 7.

%o (PARI) al(n) = my(r=vector(n),pps=[p| p <- [1..n], isprimepower(p)],p2); for(k=1,#pps,p2=2^(k-1);forstep(j=pps[k],n,pps[k],r[j]+=p2));r

%o (Haskell)

%o a248906 = sum . map ((2 ^) . subtract 2 . a095874) . tail . a210208_row

%o -- _Reinhard Zumkeller_, Mar 07 2015

%Y Cf. A246655, A065515, A034729, A000961.

%Y Cf. A095874, a210208, A073093, A000079.

%K nonn

%O 1,3

%A _Franklin T. Adams-Watters_, Mar 06 2015

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)